Should we ‘control for’ everything when running regressions? No way!16 September, 2015 at 12:55 | Posted in Statistics & Econometrics | 1 Comment
When I present this argument … one or more scholars say, “But shouldn’t I control for everything I can in my regressions? If not, aren’t my coefficients biased due to excluded variables?” This argument is not as persuasive as it may seem initially. First of all, if what you are doing is misspecified already, then adding or excluding other variables has no tendency to make things consistently better or worse … The excluded variable argument only works if you are sure your specification is precisely correct with all variables included. But no one can know that with more than a handful of explanatory variables.
Still more importantly, big, mushy linear regression and probit equations seem to need a great many control variables precisely because they are jamming together all sorts of observations
that do not belong together. Countries, wars, racial categories, religious preferences, education levels, and other variables that change people’s coefficients are “controlled” with dummy variables that are completely inadequate to modeling their effects. The result is a long list of independent variables, a jumbled bag of nearly unrelated observations, and often a hopelessly bad specification with meaningless (but statistically significant with several
A preferable approach is to separate the observations into meaningful subsets—internally compatible statistical regimes … If this can’t be done, then statistical analysis can’t be done. A researcher claiming that nothing else but the big, messy regression is possible because, after all, some results have to be produced, is like a jury that says, “Well, the evidence was weak, but somebody had to be convicted.”